Answer:
(x - 6)(3x + 15) + 95
Explanation:
Here's the long division of (3x^2 - 3x + 5) ÷ (x - 6):
3x + 15
--------------
x - 6 | 3x^2 - 3x + 5
- (3x^2 - 18x)
--------------
15x + 5
- (15x - 90)
------------
95
Therefore, the quotient is 3x + 15, and the remainder is 95.
The quotient represents the result of the division of the polynomial (3x^2 - 3x + 5) by the divisor (x - 6). In particular, the quotient 3x + 15 represents the linear polynomial that, when multiplied by the divisor x - 6, gives the dividend 3x^2 - 3x + 5.
In other words, we have:
(3x^2 - 3x + 5) = (x - 6)(3x + 15) + 95
The remainder 95 indicates that the division is not exact, and that there is a "leftover" term of 95 when we try to divide the polynomial (3x^2 - 3x + 5) by (x - 6).